To determine the appropriate inequality for a person to be classified as underweight based on their Body Mass Index (BMI), we need to understand the classification criteria for underweight.
The Body Mass Index (BMI) is a measure that uses a person’s weight and height to determine their weight category. The formula for BMI is given by:
[tex]\[ \text{BMI} = \frac{\text{weight (kg)}}{\text{height (m)}^2} \][/tex]
According to health standards, different BMI ranges classify a person's weight status:
- Underweight: BMI less than 18.5
- Normal weight: BMI from 18.5 to 24.9
- Overweight: BMI from 25 to 29.9
- Obesity: BMI of 30 or greater
For a person to be classified as underweight, their BMI must be less than 18.5.
Let's go through each of the provided inequalities:
1. [tex]\( BMI < 18.5 \)[/tex]: This inequality states that the BMI is less than 18.5, which fits the criteria for being classified as underweight.
2. [tex]\( BMI \geq 18.5 \)[/tex]: This inequality states that the BMI is 18.5 or greater, which would classify a person as normal weight, overweight, or obese, but not underweight.
3. [tex]\( BMI > 18.5 \)[/tex]: This inequality states that the BMI is greater than 18.5, which excludes the underweight classification.
4. [tex]\( BMI \leq 18.5 \)[/tex]: This inequality states that the BMI is less than or equal to 18.5. While it includes the underweight category, it also includes 18.5, which is the threshold for normal weight.
Given the criteria for classifying someone as underweight, the correct inequality must be:
[tex]\[ BMI < 18.5 \][/tex]
Thus, the appropriate inequality for classifying a person as underweight is:
[tex]\[ \boxed{BMI < 18.5} \][/tex]
